An engine expends $40.0 \mathrm{hp}$ in moving a car along a level track at a speed of $15.0 \mathrm{~m} / \mathrm{s}$. How large is the total force acting on the car in the direction opposite to the motion of the car?

Is each of the following statements true or false? b) More power is required to lift a box slowly than to lift a box quickly.

Is each of the following statements true or false? a) Work cannot be done in the absence of motion.

A car of mass 1214.5 kg is moving at a speed of 62.5 mph when it misses a curve in the road and hits a bridge piling. If the car comes to rest in 0.236 s, how much average power (in watts) is expended in this interval?

While a boat is being towed at a speed of $12.0 \mathrm{~m} / \mathrm{s}$, the tension in the towline is $6.00 \mathrm{kN}$. What is the power supplied to the boat through the towline?

The damage done by a projectile on impact is correlated with its kinetic energy. Calculate and compare the kinetic energies of these three projectiles: a) a $10.0-\mathrm{kg}$ stone at $30.0 \mathrm{~m} / \mathrm{s}$.

A horse draws a sled horizontally across a snow-covered field. The coefficient of friction between the sled and the snow is $0.195$, and the mass of the sled, including the load, is $202.3 \mathrm{~kg}$. If the horse moves the sled at a constant speed of $1.785 \mathrm{~m} / \mathrm{s}$, what is the power needed to accomplish this?

A spring with a spring constant of $238.5 \mathrm{~N} / \mathrm{m}$ is compressed by $0.231 \mathrm{~m}$. Then a steel ball bearing of mass $0.0413 \mathrm{~kg}$ is put against the end of the spring, and the spring is released. What is the speed of the ball bearing right after it loses contact with the spring? (The ball bearing will come off the spring exactly as the spring returns to its equilibrium position. Assume that the mass of the spring can be neglected.)

A spring with spring constant $k$ is initially compressed a distance $x_0$ from its equilibrium length. After returning to its equilibrium position, the spring is then stretched a distance $x_0$ from that position. What is the ratio of the work that needs to be done on the spring in the stretching to the work done in the compressing?

A spring is stretched 5.00 cm from its equilibrium position. If this stretching requires 30.0 J of work, what is the spring constant?

An ideal spring has the spring constant $k=440$. $\mathrm{N} / \mathrm{m}$. Calculate the distance this spring must be stretched from its equilibrium position for $25.0 \mathrm{~J}$ of work to be done.

A force given by $\vec{F}(x)=5 x^3 \hat{x}$ (in $\mathrm{N} / \mathrm{m}^3$ ) acts on a 1.00-kg mass moving on a frictionless surface. The mass moves from $x=2.00 \mathrm{~m}$ to $x=6.00 \mathrm{~m}$. b) If the mass has a speed of $2.00 \mathrm{~m} / \mathrm{s}$ at $x=2.00 \mathrm{~m}$, what is its speed at $x=6.00 \mathrm{~m} ?$

A force given by $\vec{F}(x)=5 x^3 \hat{x}$ (in $\mathrm{N} / \mathrm{m}^3$ ) acts on a 1.00-kg mass moving on a frictionless surface. The mass moves from $x=2.00 \mathrm{~m}$ to $x=6.00 \mathrm{~m}$. a) How much work is done by the force?

A body of mass $m$ moves along a trajectory $\vec{r}(t)$ in three-dimensional space with constant kinetic energy. What geometric relationship has to exist between the body's velocity vector, $\vec{v}(t)$, and its acceleration vector, $\vec{a}(t)$, in order to accomplish this ?